Answer:
There are 1,039,584 ways in which this can be done.
Step-by-step explanation:
Total number of black marbles = 17
Total number of blue marbles = 9
The number black marbles to be chosen = 6
The number blue marbles to be chosen = 3
So, we have to choose 6 black from 17 black marbles.
and to choose 3 blue from 9 blue marbles.
So, the number if possible ways to do it : ![^{17} \textrm{C}_ {6} \times ^{9} \textrm{C}_ {3}](https://tex.z-dn.net/?f=%5E%7B17%7D%20%20%5Ctextrm%7BC%7D_%20%7B6%7D%20%20%5Ctimes%20%5E%7B9%7D%20%20%5Ctextrm%7BC%7D_%20%7B3%7D)
![^{n} \textrm{C}_ {r} = \frac{n! }{r! (n-r)!}](https://tex.z-dn.net/?f=%5E%7Bn%7D%20%20%5Ctextrm%7BC%7D_%20%7Br%7D%20%20%3D%20%5Cfrac%7Bn%21%20%7D%7Br%21%20%28n-r%29%21%7D)
Now, solving
, we get:
![^{17} \textrm{C}_ {6} = \frac{17!}{6! \times 11!} \\= \frac{17 \times 16 \times 15 \times 14\times 13\times 12 \times 11! }{11! \times (6\times 5 \times 4 \times 3\times 2)} = 12,376](https://tex.z-dn.net/?f=%5E%7B17%7D%20%20%5Ctextrm%7BC%7D_%20%7B6%7D%20%20%3D%20%5Cfrac%7B17%21%7D%7B6%21%20%5Ctimes%2011%21%7D%20%20%5C%5C%3D%20%5Cfrac%7B17%20%5Ctimes%2016%20%5Ctimes%2015%20%5Ctimes%2014%5Ctimes%2013%5Ctimes%2012%20%5Ctimes%2011%21%20%7D%7B11%21%20%5Ctimes%20%286%5Ctimes%205%20%5Ctimes%204%20%5Ctimes%203%5Ctimes%202%29%7D%20%20%20%3D%2012%2C376)
solving
, we get:
![^{9}\textrm{C}_{3} = \frac{9!}{6! \times 3!}\\= \frac{9 \times 8 \times 7 \times 6! }{6!\times (3\times 2 )} = 84](https://tex.z-dn.net/?f=%5E%7B9%7D%5Ctextrm%7BC%7D_%7B3%7D%20%20%3D%20%5Cfrac%7B9%21%7D%7B6%21%20%5Ctimes%203%21%7D%5C%5C%3D%20%5Cfrac%7B9%20%5Ctimes%208%20%5Ctimes%207%20%20%5Ctimes%206%21%20%7D%7B6%21%5Ctimes%20%283%5Ctimes%202%20%29%7D%20%3D%2084)
![\implies^{17}\textrm{C}_ {6}\times ^{9} \textrm{C}_ {3}=12,376 \times 84 = 1,039,584](https://tex.z-dn.net/?f=%5Cimplies%5E%7B17%7D%5Ctextrm%7BC%7D_%20%7B6%7D%5Ctimes%20%5E%7B9%7D%20%20%5Ctextrm%7BC%7D_%20%7B3%7D%3D12%2C376%20%5Ctimes%2084%20%3D%201%2C039%2C584)
Hence, there are 1,039,584 ways in which this can be done.
Y intercept when x = 0
f(x) = (1/2)^0 = 1
so
y intercept (0,1)
answer
C. (0,1)
Answer:
Step-by-step explanation:
first you have to figure out how much room is in the classroom
then you are going to have measure 2 mters apart of each table
Answer:
The formula for the surface area of a prism is obtained by taking the sum of (twice the base area) and (the lateral surface area of the prism). The surface area of a prism is given as S
<h2>= (2 × Base Area) + (Base perimeter × height)</h2>
where "S" is the surface area of the prism.
Answer:
![sin(t)=\frac{\sqrt{99}}{10}](https://tex.z-dn.net/?f=sin%28t%29%3D%5Cfrac%7B%5Csqrt%7B99%7D%7D%7B10%7D)
Step-by-step explanation:
Remember that
If angle t belong to the First Quadrant
then
The value of sin(t) and cos(t) are positive values
we know that
---> by trigonometric identity
we have
![cos(t)=0.1=\frac{1}{10}](https://tex.z-dn.net/?f=cos%28t%29%3D0.1%3D%5Cfrac%7B1%7D%7B10%7D)
substitute
![sin^2(t)+(\frac{1}{10})^2=1](https://tex.z-dn.net/?f=sin%5E2%28t%29%2B%28%5Cfrac%7B1%7D%7B10%7D%29%5E2%3D1)
![sin^2(t)+\frac{1}{100}=1](https://tex.z-dn.net/?f=sin%5E2%28t%29%2B%5Cfrac%7B1%7D%7B100%7D%3D1)
![sin^2(t)=1-\frac{1}{100}](https://tex.z-dn.net/?f=sin%5E2%28t%29%3D1-%5Cfrac%7B1%7D%7B100%7D)
![sin^2(t)=\frac{99}{100}](https://tex.z-dn.net/?f=sin%5E2%28t%29%3D%5Cfrac%7B99%7D%7B100%7D)
![sin(t)=\frac{\sqrt{99}}{10}](https://tex.z-dn.net/?f=sin%28t%29%3D%5Cfrac%7B%5Csqrt%7B99%7D%7D%7B10%7D)